Zero-temperature coarsening in the 2d Potts model
Zero-temperature coarsening in the 2d Potts model
复制标题
二维 Potts 模型中的零温度粗化
DOI：
10.1088/1742-5468/2013/06/p06018
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
D. Udler
中科院分区：
文献类型：
--
作者：
V. Fradkov;D. Udler
我们研究了突然淬火至零度后二维动力学q态波茨模型的命运。基态和复杂静态均以非零概率达到。这些结果类似于在二维Ising模型的淬火中发现的结果；然而，q-state Potts模型（q≥3）中的静态状态的多样性比Ising模型丰富得多，后者的静态状态要么是基态，要么是条纹态。另一种可能性是，波茨系统被困在一组等能闪烁状态中，其中一组自旋可以无限地翻转；这些状态与三维Ising模型的淬火状态相似。向最终能量的演化也是不寻常的——在很长一段时间内，可能会发生突然和大量的能量下降，并伴随着宏观的畴结构重排序。动力学波茨模型的零温度淬火的这种不确定性与相序动力学理论的基本预测不一致。我们还提出了具有两个以上等效基态的连续统描述。由此产生的随时间变化的金兹堡-朗道方程再现了动态波茨模型淬火时产生的复杂簇模式。
We study the fate of the 2d kinetic q-state Potts model after a sudden quench to zero temperature. Both ground states and complicated static states are reached with non-zero probabilities. These outcomes resemble those found in the quench of the 2d Ising model; however, the variety of static states in the q-state Potts model (with q ≥ 3) is much richer than in the Ising model, where static states are either ground or stripe states. Another possibility is that the Potts system gets trapped on a set of equal-energy blinker states, where a subset of spins can flip ad infinitum; these states are similar to those found in the quench of the 3d Ising model. The evolution towards the final energy is also unusual—at long times, sudden and massive energy drops may occur that are accompanied by macroscopic reordering of the domain structure. This indeterminacy in the zero-temperature quench of the kinetic Potts model is at odds with basic predictions from the theory of phase-ordering kinetics. We also propose a continuum description of coarsening with more than two equivalent ground states. The resulting time-dependent Ginzburg–Landau equations reproduce the complex cluster patterns that arise in the quench of the kinetic Potts model.